Numerical solution of the hydrodynamics problem with a curved interphase boundary
DOI:
https://doi.org/10.7242/1999-6691/2013.6.3.40Keywords:
Navier–Stokes equations, curvilinear interphase boundary, discontinuous coefficientsAbstract
In this paper, we develop an approximate method and perform the numerical analysis of the mathematical model, obtained by sampling in time and linearizing the problem of a two-phase viscous fluid flow. We assume that the fluid is incompressible, phase mixing is absent, and the interphase boundary varies with time. The problem is formulated based on incompressible Navier-Stokes equations taking into account these constraints.
Downloads
References
Chang Y.C., Hou T.Y., Merrimam B., Osher S. A level set formulation of Eulerian interface captured methods for incompressible fluid flows // J. Comput. Phys. - 1996. - V. 124. - P. 449-464. DOI
2. Rukavisnikov A.V. Obobsennaa postanovka zadaci tecenia dvuhfaznoj zidkosti s nepreryvno izmenausimsa interfejsom // Matem. modelirovanie. - 2008. - T. 20, No 3. - S. 3-8.
3. Drazin P.G., Reid W.H. Hydrodynamic stability. - Cambridge, UK: Cambridge University Press, 2004. - 605 p.
4. Bernardi C., Maday Y., Patera A. A new nonconforming approach to domain decomposition: the mortar element method // Nonlinear Partial Differential Equations and Their Applications. College de France Seminar, V. XI / Ed. H. Brezis et al. - Paris: Pitman, 1994. - P. 13-51.
5. Flemisch B., Melenk J.M., Wohlmuth B.I. Mortar methods with curved interfaces // Appl. Numer. Math. - 2005. - V. 54, N. 3-4. - P. 339-361. DOI
6. Belgacem F.B. The mixed mortar finite element method for the incompressible Stokes problem: convergence analysis // SIAM J. Numer. Anal. - 2000. - V. 37, N. 4. - P. 1085-1100. DOI
7. Rukavisnikov A.V., Rukavisnikov V.A. Nekonformnyj metod konecnyh elementov dla zadaci Stoksa s razryvnym koefficientom // Sib. zurn. industr. matem. - 2007. - T. 10, No 4. - S. 104-117.
8. Rukavisnikov A.V. O postroenii cislennogo metoda dla zadaci Stoksa s razryvnym koefficientom vazkosti // ZVT. - 2009. - T. 14, No 2. - S. 110-123.
9. Rukavisnikov A.V. Nekonformnyj metod konecnyh elementov dla odnoj zadaci gidrodinamiki s krivolinejnym interfejsom // ZVMMF. - 2012. - T. 52, No 6. - S. 1072-1094.
10. Olshanskii M.A., Reusken A. Grad-div stabilization for Stokes equations// Math. Comput. - 2004. - V. 73, N. 248. - P. 1699-1718. DOI
11. Sedov L.I. Mehanika splosnoj sredy. - M.: Nauka, 1970. - T. 2. - 568 s.
12. Elman H.C., Silvester D.J., Wathen A.J. Finite elements and fast iterative solvers: with applications in incompressible fluid dynamics. - Oxford, UK: Oxford University Press, 2005. - 413 p.
13. S"arle F. Metod konecnyh elementov dla ellipticeskih zadac. - M.: Mir, 1980. - 512 s.
14. Brezzi F., Fortin M. Mixed and hybrid finite element methods. - New York: Springer-Verlag, 1991. - 368 p.
15. Bramble J.H., Pasciak J.E., Vassilev A.T. Analysis of the inexact Uzawa algorithm for saddle point problems // SIAM J. Numer. Anal. - 1997. - V. 34, N. 3. - P. 1072-1092. DOI
16. Saad Y. Iterative methods for sparse linear systems. - New Jersey: PWS Pub. Co., 1996. - 450 p.
17. Il’in V.P. Metody konecnyh raznostej i konecnyh ob"emov dla ellipticeskih uravnenij. - Novosibirsk: Izd-vo IM SO RAN, 2000. - 345 s.
18. Little L., Saad Y., Smoch L. Block LU preconditioners for symmetric and nonsymmetric saddle point problems // SIAM J. Sci. Comput. - 2003. - V. 25, N. 2. - P. 729-748. DOI
19. Grisvard P. Elliptic problems in nonsmooth domains. - Boston: Pitman, 1985. - 410 p.
Downloads
Published
Issue
Section
License
Copyright (c) 2013 Computational Continuum Mechanics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.